Results 21 to 30 of about 1,238 (267)
Ninety-Six Distinct Real Matrices for Representing a Quaternion Number
Journal of Mathematics, 2020 In this paper, we investigate on the number of all possible real matrices representing a quaternion number as three 4×4 skew-symmetric matrices plus the identity matrix of order 4, and how to determine these matrices.
W. E. Ahmed
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Review of Quaternion-Based Color Image Processing Methods
Mathematics, 2023 Images are a convenient way for humans to obtain information and knowledge, but they are often destroyed throughout the collection or distribution process.
Chaoyan Huang, Juncheng Li, Guangwei Gao
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New Insight into Quaternions and Their Matrices
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2021 The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced.
Gülsüm Yeliz ŞENTÜRK +2 more
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Journal of Applied Mathematics, 2014 Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the
Shi-Fang Yuan
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Analogies between random matrix ensembles and the one-component plasma in two-dimensions
Nuclear Physics B, 2016 The eigenvalue PDF for some well known classes of non-Hermitian random matrices — the complex Ginibre ensemble for example — can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains.
Peter J. Forrester
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Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales
Open Mathematics, 2020 In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex ...
Li Zhien, Wang Chao
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Some properties of complex quaternion and complex split quaternion matrices [PDF]
Miskolc Mathematical Notes, 2019 The aim of this study is to investigate some properties of complex quaternion and complex split quaternion matrices. To verify this, we use 2x2 complex matrix representation of these quaternions. Moreover, we present a method to find the determinant of complex quaternion and complex split quaternion matrices.
Alagoz, Y., Ozyurt, G.
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On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem
MathematicsThe application of eigenvalue theory to dual quaternion Hermitian matrices holds significance in the realm of multi-agent formation control. In this paper, we study the use of Rayleigh quotient iteration (RQI) for solving the right eigenpairs of dual ...
Shan-Qi Duan +2 more
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Boundary Value Problems, 2023 This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential equations (QDEs).
Jie Liu, Siyu Sun, Zhibo Cheng
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Quaternions and matrices of quaternions
Linear Algebra and its Applications, 1997 The author gives a useful survey on quaternions and matrices of quaternions. He recalls standard facts going back to Rowan Hamilton as well as new results motivated by applications in physical theories. The main research problem presented in the paper is to extend the classical matrix theory from complex to the quaternion matrices.
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